Restricting the number of attractive physical "bonds" that can form
between particles in a fluid suppresses the usual demixing phase
transition to very low particle concentrations, allowing for the
formation of open, percolated, and homogeneous states, aptly called
equilibrium or "empty" gels. Most demonstrations of this concept have
directly limited the microscopic particle valence via anisotropic
(patchy) attractions; however, an alternative macroscopic valence
limitation would be desirable for greater experimental tunability and
responsiveness. One possibility, explored in this paper, is to employ
primary particles with attractions mediated via a secondary species of
linking particles. In such a system, the linker-to-primary particle
ratio serves as a macroscopic control parameter for the average
microscopic valence. We show that the phase behavior of such a system
predicted by Wertheim's first order perturbation theory is consistent
with equilibrium gel formation: the primary particle concentrations
corresponding to the two-phase demixing transition are significantly
suppressed at both low and high linker-to-primary particle ratios.
Extensive molecular dynamics simulations validate these theoretical
predictions but also reveal the presence of loops of bonded particles,
which are neglected in the theory. Such loops cause densification and
inhibit percolation, and hence the range of viable empty gel state
conditions is somewhat reduced relative to the Wertheim theory
predictions. Published by AIP Publishing.